As we stress in Section 2, interpreting these graphs is not easy because cohort, age and time are perfectly collinear variables. Their distinct effects are not identified: for instance, any interpretation of the data in terms of age and cohort effects (normalizing time effects to zero) can be recast in terms of an alternative decomposition in terms of age and time effects (normalizing cohort effects to zero). Nonetheless, some features of the raw data are highly suggestive.

Interestingly, the absolute level of the variance is considerably higher in the US (0.4 on average), lowest in Italy (0.25) and intermediate in the UK (0.3), reflecting very different patterns of consumption inequality in these countries. In the UK there is some evidence of cohort effects, especially for households born after the Second World War (cohorts 7 to 10 in Figure 1). In the US and Italy cohort effects are absent or weak at best. In the UK and Italy the variance of log consumption increases up to age 60, and diminishes for older households, which Deaton and Paxson interpret as evidence in support of models with finite horizon, where income shocks cease after retirement. The graph for the US, by contrast, is much flatter over the entire life-cycle.

In Figures 4, 5 and 6 we plot the cross-sectional variance for consumption defined in terms of adult equivalent, assuming an intertemporal elasticity of substitution of 0.8 (see equation 10). The behavior of these variances is rather different than in the previous figures in all three countries. First of all, the variance is now considerably smaller, especially in the UK. Second, the age pattern is much flatter than in the previous set of figures suggesting that variation in household size and composition over the life-cycle explains a good part of the age-profile of the cross-sectional variance of consumption. In the UK and the US there is no evidence of the spreading of consumption over the life-cycle. In Italy the cross-sectional variance declines slightly with the age of the household head, reversing the pattern in Figure 3.